Dr. Ara B. Dopsis and Dr. C. Ellie Gans are performing genetic crosses on daisy plants. They self-fertilize a blueflowered daisy and grow 100 progeny plants that consist of 55 blue-flowered plants, 22 purple-flowered plants, and 23 white-flowered plants. Dr. Dopsis believes this is the result of segregation of two alleles at one locus and that the progeny ratio is 1:2:1. Dr. Gans thinks the progeny phenotypes are the result of two epistatic genes and that the ratio is 9:3:4. The two scientists ask you to resolve their conflict by performing chi-square analysis on the data for both proposed genetic mechanisms:

Calculate the chi square statistic x2 by completing the following steps:

For each observed number;

1. subtract the corresponding expected number (O - E).

2. Square the difference [ (O - E) 2 ].

3. Divide the squares obtained for each cell in the table by the expected number for that cell [ (O - E) 2 / E ].

4. Sum all the values for (O - E) 2 / E. This is the chi square statistic.

Explanation:

A chi square (X²) statistic is used to investigate whether distributions of categorical variables differ from one another. Basically categorical variable yield data in the categories and numerical variables yield data in numerical form. The Chi Square statistic compares the tallies or counts of categorical responses between two (or more) independent groups. (note: Chi square tests can only be used on actual numbers and not on percentages, proportions, means, etc.)

Calculate chi square for the 1:2:1 hypothesis of Dr. Ara B. Dopsis

Observed

Blue 55

Purple 22

White 23

Expected values 1:2:1 are 50, 25 and 25

calculate chi square for the 9:3:4 hypothesis of Dr. Gans.

Phenotype Observed

Blue 55

Purple 22

White 23

Expected values 9:3:4 are 56, 19, 25

The formula to calculate chi-square value is as follows:

Chi - Square value = ((O - E) ^2) / E

Where,

O = observed Value

E = expected value

The chi square test by using the ratio 1:2:1 is as follows:

By calculation using the chi - square formula above, we obtain

Steps:

Subtract each expected value (E) from corresponding observed value (O).

(O - E)

Square all the results (O - E) ^2

Sum all the results of square values.

Divide the sum by the expected value (E)

The results:

chi-square value = 1.02

The degrees of freedom = 3 - 1 = 2

By taking significance level

p < 0.05, the P-Value is 0.68

It can be concluded that the result is not significant at 0.05.

It is consistent with 1:2:1 ratio and hypothesis cannot be rejected.

Secondly,

The chi square test by using the ratio 9:3:4 is as follows:

By calculation,

chi-square value = 0.75

The degrees of freedom = 3 - 1 = 2

Also, by taking significance level 0.05

The P-Value is 0.68

It can be concluded that the result is not significant at 0.05

It is consistent with the ratio 9:3:4 and hypothesis cannot be rejected.